[1]} and [2]} present an optimality result in the context of conformal prediction. Roughly, given any valid, nested, and permutation invariant prediction region, there exists a non-conformity measure such that the corresponding conformal prediction region derived from it is at least as efficient. More precisely, if \({C}_\alpha (y^n)\)  represents a valid and nested \(100(1-\alpha )\) % prediction region for each \(\alpha \in [0,1]\) , then there exists a nonconformity measure—determined by a mapping \(\Psi \) —whose corresponding \(100(1-\alpha )\) % conformal prediction region \({P}_\alpha (y^n) = {P}_\alpha (y^n; \Psi )\)  satisfies
\( {P}_\alpha (y^n) \subseteq {C}_\alpha (y^n), \quad \text{for all $y^n$ and all $\alpha \in [0,1]$}. \) 
